{
  "title": "Properties of Integers (Integers) - Grade 7 ICSE",
  "total_questions": 60,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "Which property: 5 + (-5) = 0? 🔢",
      "options": {
        "A": "Closure",
        "B": "Commutative",
        "C": "Associative",
        "D": "Additive Inverse"
      },
      "correct_answer": "D"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "8 × 1 = 8 shows which property? ✖️",
      "options": {
        "A": "Closure",
        "B": "Multiplicative Identity",
        "C": "Commutative",
        "D": "Associative"
      },
      "correct_answer": "B"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "(-3) + 7 = 7 + (-3) shows? ➕",
      "options": {
        "A": "Closure",
        "B": "Commutative",
        "C": "Associative",
        "D": "Distributive"
      },
      "correct_answer": "B"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "Which is additive identity for integers? 0️⃣",
      "options": { "A": "1", "B": "-1", "C": "0", "D": "None" },
      "correct_answer": "C"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "(-4) × 0 = 0 shows? 0️⃣",
      "options": {
        "A": "Multiplicative Identity",
        "B": "Zero Property",
        "C": "Closure",
        "D": "Inverse"
      },
      "correct_answer": "B"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "3 × (4 + 5) = 3×4 + 3×5 shows? 📐",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Closure"
      },
      "correct_answer": "C"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "(-2) + [3 + (-5)] = [(-2) + 3] + (-5) shows? 🔄",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Closure"
      },
      "correct_answer": "B"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "Multiplicative inverse of -7 is? 🔄",
      "options": { "A": "7", "B": "1/7", "C": "-1/7", "D": "1" },
      "correct_answer": "C"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "(-8) × 1/(-8) = 1 shows? ✖️",
      "options": {
        "A": "Multiplicative Identity",
        "B": "Multiplicative Inverse",
        "C": "Commutative",
        "D": "Associative"
      },
      "correct_answer": "B"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "Sum of integer and its additive inverse is? ➕",
      "options": { "A": "1", "B": "0", "C": "-1", "D": "Same integer" },
      "correct_answer": "B"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "Product of integer and its multiplicative inverse is? ✖️",
      "options": { "A": "0", "B": "1", "C": "-1", "D": "Same integer" },
      "correct_answer": "B"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "(-5) × 6 = 6 × (-5) shows? 🔄",
      "options": {
        "A": "Closure",
        "B": "Commutative",
        "C": "Associative",
        "D": "Distributive"
      },
      "correct_answer": "B"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "Which is true for integers under addition? ➕",
      "options": {
        "A": "Not closed",
        "B": "No commutative",
        "C": "Always closed",
        "D": "No associative"
      },
      "correct_answer": "C"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "(-9) + 0 = -9 shows? 0️⃣",
      "options": {
        "A": "Additive Identity",
        "B": "Additive Inverse",
        "C": "Commutative",
        "D": "Associative"
      },
      "correct_answer": "A"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "4 × (-2 × 3) = (4 × -2) × 3 shows? 📐",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Closure"
      },
      "correct_answer": "B"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "Additive inverse of 15 is? 🔄",
      "options": { "A": "15", "B": "1/15", "C": "-15", "D": "-1/15" },
      "correct_answer": "C"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "(-12) × 1 = -12 shows? 1️⃣",
      "options": {
        "A": "Multiplicative Identity",
        "B": "Multiplicative Inverse",
        "C": "Zero Property",
        "D": "Closure"
      },
      "correct_answer": "A"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "5 × (6 - 2) = 5×6 - 5×2 shows? ➖",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Closure"
      },
      "correct_answer": "C"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "Multiplicative inverse of -1/8 is? 🔄",
      "options": { "A": "8", "B": "-8", "C": "1/8", "D": "-1/8" },
      "correct_answer": "B"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "(-20) + 20 = 0 shows? 🔢",
      "options": {
        "A": "Additive Identity",
        "B": "Additive Inverse",
        "C": "Commutative",
        "D": "Associative"
      },
      "correct_answer": "B"
    },
    {
      "id": 21,
      "difficulty": "medium",
      "question": "Verify: (-8) × [5 + (-3)] = (-8)×5 + (-8)×(-3). Which property? 📊",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Closure"
      },
      "correct_answer": "C"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "If a × (b + c) = a×b + a×c for all integers, which property? 📐",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Identity"
      },
      "correct_answer": "C"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "Name property: (-25) + 25 = 25 + (-25) = 0 🔄",
      "options": {
        "A": "Commutative & Additive Inverse",
        "B": "Associative only",
        "C": "Distributive only",
        "D": "Closure only"
      },
      "correct_answer": "A"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "Which property justifies: (-7) × [(-3) × 4] = [(-7) × (-3)] × 4? 🧮",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Identity"
      },
      "correct_answer": "B"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "If a, b, c are integers, a × (b - c) = a×b - a×c shows? ➖",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Closure"
      },
      "correct_answer": "C"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "Name all properties in: (-4) × [(-2) + 3] = (-4)×(-2) + (-4)×3 📝",
      "options": {
        "A": "Distributive only",
        "B": "Commutative & Distributive",
        "C": "Associative & Distributive",
        "D": "Closure & Distributive"
      },
      "correct_answer": "A"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "Which is NOT true for integers? ❌",
      "options": {
        "A": "a + b = b + a",
        "B": "a × b = b × a",
        "C": "a - b = b - a",
        "D": "a + 0 = a"
      },
      "correct_answer": "C"
    },
    {
      "id": 28,
      "difficulty": "medium",
      "question": "Verify property: (-9) × [10 + (-2)] = (-9)×10 + (-9)×(-2) ✅",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Identity"
      },
      "correct_answer": "C"
    },
    {
      "id": 29,
      "difficulty": "medium",
      "question": "If (-x) is additive inverse of x, then x + (-x) = ? ➕",
      "options": { "A": "1", "B": "0", "C": "-1", "D": "x" },
      "correct_answer": "B"
    },
    {
      "id": 30,
      "difficulty": "medium",
      "question": "Which property: a + b = b + a for all integers a, b? 🔄",
      "options": {
        "A": "Closure",
        "B": "Commutative",
        "C": "Associative",
        "D": "Identity"
      },
      "correct_answer": "B"
    },
    {
      "id": 31,
      "difficulty": "medium",
      "question": "Name property: (a × b) × c = a × (b × c) 📐",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Identity"
      },
      "correct_answer": "B"
    },
    {
      "id": 32,
      "difficulty": "medium",
      "question": "If 1/a is multiplicative inverse of a (a≠0), then a × 1/a = ? ✖️",
      "options": { "A": "0", "B": "1", "C": "a", "D": "1/a" },
      "correct_answer": "B"
    },
    {
      "id": 33,
      "difficulty": "medium",
      "question": "Which property ensures sum of two integers is always integer? ➕",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Closure",
        "D": "Identity"
      },
      "correct_answer": "C"
    },
    {
      "id": 34,
      "difficulty": "medium",
      "question": "(-5) × (6 + (-4)) = (-5)×6 + (-5)×(-4) shows? 📊",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Closure"
      },
      "correct_answer": "C"
    },
    {
      "id": 35,
      "difficulty": "medium",
      "question": "Multiplicative inverse of -2/3 is? 🔄",
      "options": { "A": "2/3", "B": "-2/3", "C": "3/2", "D": "-3/2" },
      "correct_answer": "D"
    },
    {
      "id": 36,
      "difficulty": "medium",
      "question": "Additive inverse of -(-5) is? 🔄",
      "options": { "A": "5", "B": "-5", "C": "1/5", "D": "-1/5" },
      "correct_answer": "B"
    },
    {
      "id": 37,
      "difficulty": "medium",
      "question": "If a, b, c are integers, a × b = b × a shows? ✖️",
      "options": {
        "A": "Closure",
        "B": "Commutative",
        "C": "Associative",
        "D": "Distributive"
      },
      "correct_answer": "B"
    },
    {
      "id": 38,
      "difficulty": "medium",
      "question": "Zero property of multiplication states: a × 0 = ? 0️⃣",
      "options": { "A": "a", "B": "0", "C": "1", "D": "-a" },
      "correct_answer": "B"
    },
    {
      "id": 39,
      "difficulty": "medium",
      "question": "Which is distributive property? 📐",
      "options": {
        "A": "a(b+c)=ab+ac",
        "B": "a+b=b+a",
        "C": "a+(b+c)=(a+b)+c",
        "D": "a+0=a"
      },
      "correct_answer": "A"
    },
    {
      "id": 40,
      "difficulty": "medium",
      "question": "Additive identity + Multiplicative identity = ? 1️⃣0️⃣",
      "options": { "A": "0", "B": "1", "C": "2", "D": "3" },
      "correct_answer": "B"
    },
    {
      "id": 41,
      "difficulty": "hard",
      "question": "Prove using properties: (-25) × [(-4) + (-6)] = (-25)×(-4) + (-25)×(-6) 📚",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "All three"
      },
      "correct_answer": "C"
    },
    {
      "id": 42,
      "difficulty": "hard",
      "question": "If a, b, c are integers and a×(b-c)=a×b - a×c, name the property used. 🔍",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Closure"
      },
      "correct_answer": "C"
    },
    {
      "id": 43,
      "difficulty": "hard",
      "question": "Find product using properties: (-8) × 45 + (-8) × 55 🧮",
      "options": { "A": "-800", "B": "-801", "C": "-802", "D": "-803" },
      "correct_answer": "A"
    },
    {
      "id": 44,
      "difficulty": "hard",
      "question": "Using distributive property, simplify: (-7) × (-12) + (-7) × (-8) 📝",
      "options": { "A": "139", "B": "140", "C": "141", "D": "142" },
      "correct_answer": "B"
    },
    {
      "id": 45,
      "difficulty": "hard",
      "question": "Prove: (-a) × (-b) = a × b using integer properties. 🔄",
      "options": {
        "A": "Distributive & Additive Inverse",
        "B": "Commutative & Identity",
        "C": "Associative & Closure",
        "D": "Multiplicative Identity only"
      },
      "correct_answer": "A"
    },
    {
      "id": 46,
      "difficulty": "hard",
      "question": "Simplify using properties: 25 × (-48) + 25 × (-52) ⚡",
      "options": { "A": "-2499", "B": "-2500", "C": "-2501", "D": "-2502" },
      "correct_answer": "B"
    },
    {
      "id": 47,
      "difficulty": "hard",
      "question": "Find sum using properties: (-17) × (-29) + (-17) × (-71) 📊",
      "options": { "A": "1699", "B": "1700", "C": "1701", "D": "1702" },
      "correct_answer": "B"
    },
    {
      "id": 48,
      "difficulty": "hard",
      "question": "Using distributive law, find: (-15) × [(-7) + (-3)] 📐",
      "options": { "A": "149", "B": "150", "C": "151", "D": "152" },
      "correct_answer": "B"
    },
    {
      "id": 49,
      "difficulty": "hard",
      "question": "Simplify: (-125) × (-41) + (-125) × (-59) using property 🧩",
      "options": { "A": "12499", "B": "12500", "C": "12501", "D": "12502" },
      "correct_answer": "B"
    },
    {
      "id": 50,
      "difficulty": "hard",
      "question": "Prove: For integers a, b, c: a × (b + c) = (b + c) × a 🔄",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Closure"
      },
      "correct_answer": "A"
    },
    {
      "id": 51,
      "difficulty": "hard",
      "question": "Find using properties: (-32) × 98 + (-32) × 2 🎯",
      "options": { "A": "-3199", "B": "-3200", "C": "-3201", "D": "-3202" },
      "correct_answer": "B"
    },
    {
      "id": 52,
      "difficulty": "hard",
      "question": "Simplify: (-76) × (-33) + (-76) × (-67) using distributive law 📝",
      "options": { "A": "7599", "B": "7600", "C": "7601", "D": "7602" },
      "correct_answer": "B"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "Prove: a × 0 = 0 × a = 0 for any integer a 0️⃣",
      "options": {
        "A": "Zero Property",
        "B": "Identity Property",
        "C": "Inverse Property",
        "D": "Closure Property"
      },
      "correct_answer": "A"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "Find product: (-21) × (-103) + (-21) × (-97) 🧮",
      "options": { "A": "4199", "B": "4200", "C": "4201", "D": "4202" },
      "correct_answer": "B"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "Using properties, simplify: (-53) × (-49) + (-53) × (-51) ⚡",
      "options": { "A": "5299", "B": "5300", "C": "5301", "D": "5302" },
      "correct_answer": "B"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "Prove: Additive inverse of additive inverse of a is a 🔄",
      "options": {
        "A": "Inverse Property",
        "B": "Identity Property",
        "C": "Closure Property",
        "D": "Commutative Property"
      },
      "correct_answer": "A"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "Simplify: (-88) × (-125) + (-88) × (-75) 📊",
      "options": { "A": "17599", "B": "17600", "C": "17601", "D": "17602" },
      "correct_answer": "B"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "Find using distributive property: (-64) × (-101) + (-64) × (-99) 📐",
      "options": { "A": "12799", "B": "12800", "C": "12801", "D": "12802" },
      "correct_answer": "B"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "Prove: (a + b) + c = a + (b + c) for integers 🧩",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Closure"
      },
      "correct_answer": "B"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "Simplify: (-99) × (-178) + (-99) × (-22) using property 🎲",
      "options": { "A": "19799", "B": "19800", "C": "19801", "D": "19802" },
      "correct_answer": "B"
    }
  ]
}